Find the distance between the pair of points (-6.-17) and (-8.-19) The distance is (Round to the nearest thousandth as needed.)

Mathematics

1 answer:

valina [46]2 years ago

3 0

Answer:

2.83

Step-by-step explanation:

d= Square root of (x2 - x1 )^2 +( y2- y1)^2

from the point given you

x1= -6

y1 = -17

x2 = -8

y2 = -19

by applying the formula

Square root of ( -8 - (-6))^2 + ( -19 - (-17))^2

Square root of (-8+6) + (-19+17)^2

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Somebody please help so I can pass, please

ASHA 777 [7]

First, we are going to find the vertex of our quadratic. Remember that to find the vertex $(h,k)$ of a quadratic equation of the form $y=a x^{2} +bx+c$ , we use the vertex formula $h= \frac{-b}{2a}$ , and then, we evaluate our equation at $h$ to find $k$ .

We now from our quadratic that $a=2$ and $b=-32$ , so lets use our formula:
$h= \frac{-b}{2a}$
$h= \frac{-(-32)}{2(2)}$
$h= \frac{32}{4}$
$h=8$
Now we can evaluate our quadratic at 8 to find $k$ :
$k=2(8)^2-32(8)+56$
$k=2(64)-256+56$
$k=128-200$
$k=-72$
So the vertex of our function is (8,-72)

Next, we are going to use the vertex to rewrite our quadratic equation:
$y=a(x-h)^2+k$
$y=2(x-8)^2+(-72)$
$y=2(x-8)^2-72$
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.

We can conclude that:
The rewritten equation is $y=2(x-8)^2-72$
The x-coordinate of the minimum is 8